Procedure Steps for Solving a Max/Min Problem Like Example 3 1) Draw a picture, if applicable. 2) Defi ne the unknowns. Label the picture. 3) Write the max/min equation. 4) Write the constraint equation. 5) Solve the constraint for a variable. Substitute the expression into the max/min equation to obtain a quadratic function. 6) Find the vertex of the parabola using the vertex formula, x b 2a . 7) Answer the question being asked. YOU TRY 3 Find the maximum area of a rectangle that has a perimeter of 28 in. 4 Graph Parabolas of the Form x a(y k)2 h Not all parabolas are functions. Parabolas can open in the x-direction as illustrated below. Clearly, these fail the vertical line test for functions. x y 5 5 5 5 x y 5 5 5 5 Parabolas that open in the y-direction, or vertically, result from the functions y a(x h)2 k or y ax2 bx c. If we interchange the x and y, we obtain the equations x a( y k)2 h or x ay2 by c. The graphs of these equations are parabolas that open in the x-direction, or horizontally. Procedure Graphing an Equation of the Form x a(y k)2 h 1) The vertex of the parabola is (h, k). (Notice, however, that h and k have changed their positions in the equation when compared to a quadratic function.) 2) The axis of symmetry is the horizontal line y k. 3) If a is positive, the graph opens to the right. If a is negative, the graph opens to the left. When graphing equations that begin with x , many earlier processes are switched when graphing. 672 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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